If the vectors a = i-j+2k, b = 2i+4j+k and c = ai+j+bk

If the vectors a = i - j + 2k, b = 2i + 4j + k and c = ai + j + bk are mutually orthogonal, then (a,b) =

  1. (-2,3)
  2. (3,-2)
  3. (-3,2)
  4. (2,-3)

Answer

a = i - j + 2k, b = 2i + 4j + k and c = ai + j + bk

Given, a, b and c are mutually orthogonal

a.c = 0

a - 1 + 2b = 0

a + 2b = 1

b.c = 0; 2a + 4 + b = 0

2a + b = -4

The correct option is C.